Friction gearing carries torque through the contact between wheels pressed together. This version calculates a torque limit at the driver shaft. Enter demand at that same shaft to compare it with the limit; a follower load must first be referred through the wheel ratio.
Friction Gearing Interactive Calculator
Vary coefficient, normal force and driver radius to compare an ideal contact torque limit with driver-side demand. The ratio and utilization describe this one comparison, not a certified design margin.
Equation Used
The tangential-force threshold is mu times normal force. Multiplying it by driver radius gives the driver-side torque limit. Compare demand at the driver shaft; the tool does not calculate a follower torque or a slipping operating state.
- Rolling contact is dry and the coefficient of friction is constant.
- Torque limit is based on the driver wheel radius.
- No allowance is included for glazing, misalignment, heat, or dynamic shock.
Torque at the driver and follower
A loading mechanism presses the wheel surfaces together. Tangential force at the contact transmits torque between their shafts. In the simple dry-contact model, the limiting force is μF_N. Below that threshold, actual contact force is set by the transmitted load rather than always reaching the limit.
The same contact force acts through different radii at the two shafts. Driver torque is F_t R_driver and follower torque is F_t R_follower. Ideal external rolling gives opposite rotation directions and speed magnitudes ω_follower/ω_driver = R_driver/R_follower. A larger follower therefore runs more slowly with correspondingly larger torque in the lossless case.
The calculator uses driver radius. The animation pairs that radius with an illustrative 100 mm follower, scales both wheels equally to fit, and keeps their rims touching. Below the estimated threshold, opposite rotation gives equal contact surface speeds. Above the threshold, a prescribed slower follower motion illustrates relative sliding without predicting its rate. The spring indicates normal loading without a spring-stiffness calculation. Colors show the driver-demand comparison, not temperature or contact pressure. The illustrative follower is not a specification for an actual drive.
Where rolling-contact transmission fits
Friction wheels avoid tooth engagement, and suitable contact geometries can provide adjustable ratios. Commercial traction drives develop this principle with multiple rollers, controlled loading and contact-specific materials or fluids. Their behavior cannot be reduced to a universal dry-friction coefficient.
For a design comparison, consider the required torque, ratio stability, contact condition, bearing reactions and control method. This tool addresses the driver-side torque threshold. It does not assign a service interval, material specification or positioning accuracy.
Driver-side force and torque limits
T_limit = μF_N R_driver, where F_N is in newtons and R_driver is in meters. The result is in N·m. Tangential Limit is μF_N. Capacity/Demand is T_limit/T_d, and Utilization is 100 T_d/T_limit. Enter T_d at the driver shaft.
At a ratio of 1, utilization is 100% and demand equals the ideal threshold. A larger ratio gives lower utilization; a smaller ratio gives utilization above 100%. These outputs are reciprocal comparisons, not independent safety checks. The coefficient is treated as constant, with no transient or thermal model.
If a load torque is specified at the follower, its ideal equivalent driver demand is T_follower R_driver/R_follower. Actual losses and acceleration require additional allowance. The page has no follower-radius input, so that conversion must be established separately.
Example: keeping torque on the same shaft
With μ = 0.60, normal force 300 N and driver radius 0.050 m, the force limit is 180 N and driver torque limit is 9 N·m. A driver demand of 6 N·m gives Capacity/Demand = 1.5 and Utilization = 66.7%.
For a hypothetical driver radius of 0.030 m and μ = 0.35, 1.8 N·m driver demand reaches the threshold at F_N = 1.8/(0.35 × 0.030) = 171.43 N. At 100 N, the threshold is 1.05 N·m; at 400 N it is 4.2 N·m. A 4 N·m driver demand at 400 N gives a ratio of only 1.05.
A hypothetical threshold twice that 4 N·m demand requires 761.90 N under these assumptions. The value is an arithmetic comparison, not a recommended preload or a guarantee against slip. With the 10 N slider increments, adjacent selectable values 760 and 770 N give 7.98 and 8.085 N·m respectively.
Across the permitted controls, torque limits span 0.005–720 N·m. With demands of 0.1–100 N·m, ratios range from 0.00005 to 7,200 and utilization from about 0.0139% to 2,000,000%. Rounded readouts can show zero for very small positive values. Slider bounds do not establish usable hardware limits.
What the contact model leaves open
A friction wheel lacks toothed-mesh clearance but can still have elastic motion, creep and gross slip. Precise positioning depends on the complete drive, feedback and load, rather than on an unconditional claim of zero backlash or unusable accuracy.
Increasing normal force raises the calculated threshold but also changes shaft reactions and contact loading. It does not automatically improve life. Likewise, slip can create heat and damage surfaces; it is not inherently harmless overload protection. Equipment-specific material, lubrication and maintenance information is needed for those decisions.
Frequently asked questions
Which shaft does Driver Torque Limit refer to?
The driver shaft, because the equation uses driver radius. Compare it with demand at that same shaft.
Can I enter torque measured at the follower?
First refer it to the driver using the actual radius ratio and relevant losses. The calculator has no follower-radius input.
Are Capacity/Demand and Utilization separate checks?
No. They are reciprocal comparisons: utilization is 100 divided by the capacity-to-demand ratio.
Does a ratio above 1 guarantee no slip?
No. It only means demand is below the threshold for the entered constant coefficient and normal force. Real contact conditions may differ.
Is normal force twice tangential force always enough?
No. The relationship depends on μ. Even the ideal threshold requires F_N = F_t/μ, before any design allowance.
Does the animation show actual slip?
No. Above the estimated threshold, slower follower motion illustrates relative sliding. Its rate is prescribed; the animation does not solve sliding dynamics or heat.
Can a friction drive be used for positioning?
That depends on the contact design, load, control and feedback. This torque model does not calculate positioning error.
Can I diagnose noise or choose a dressing interval here?
No. The tool does not model vibration or wear. Use the actual drive’s inspection and maintenance requirements.
Friction and rolling references
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